Question: $h(x) = -3x$ $g(t) = -t^{2}-6t-6-4(h(t))$ $ h(g(8)) = {?} $
Solution: First, let's solve for the value of the inner function, $g(8)$ . Then we'll know what to plug into the outer function. $g(8) = -8^{2}+(-6)(8)-6-4(h(8))$ To solve for the value of $g$ , we need to solve for the value of $h(8)$ $h(8) = (-3)(8)$ $h(8) = -24$ That means $g(8) = -8^{2}+(-6)(8)-6+(-4)(-24)$ $g(8) = -22$ Now we know that $g(8) = -22$ . Let's solve for $h(g(8))$ , which is $h(-22)$ $h(-22) = (-3)(-22)$ $h(-22) = 66$